Definition: You are given a question on college mathematics. You are also given 4 answer options (associated with "A", "B", "C", "D"), out of which only one is correct. You need to answer the question by selecting the correct option. You should only answer with the choice letter, not the whole answer.
Input: Suppose A is a 3 × 3 matrix such that det(A − λI) = −λ^3 + 3λ^2 + λ − 3, where I is the 3 × 3 identity matrix. Which of the following are TRUE of A?
I. The trace of A is 3.
II. The determinate of A is −3.
III. The matrix A has eigenvalues −3 and 1.
(A)I only (B)II only (C)III only (D)I and II only

D